IMEX Large Time Step Finite Volume Methods for Low Froude Number Shallow Water Flows (Communications in Computational Physics, 2014)
We present new large time step methods for the shallow water flows in thelow Froude number limit. In order to take into account multiscale phenomena that typicallyappear in geophysical flows nonlinear fluxes are split into a linear part governingthe gravitational waves and the nonlinear advection. We propose to approximate fastlinear waves implicitly in time and in space by means of a genuinely multidimensionalevolution operator. On the other hand, we approximate nonlinear advection part explicitlyin time and in space by means of the method of characteristics or some standardnumerical flux function. Time integration is realized by the implicit-explicit (IMEX)method. We apply the IMEX Euler scheme, two step Runge Kutta Cranck Nicolsonscheme, as well as the semi-implicit BDF scheme and prove their asymptotic preservingproperty in the low Froude number limit. Numerical experiments demonstratestability, accuracy and robustness of these new large time step finite volume schemeswith respect to small Froude number.